The Penrose-Fife phase-field model with dynamic boundary conditions

TL;DR

This paper extends the Penrose-Fife phase-field model by incorporating dynamic boundary conditions to account for wall interactions, and analyzes the well-posedness and long-term behavior of the resulting PDE system.

Contribution

It introduces a thermodynamically consistent extension of the phase-field model with dynamic boundary conditions and studies its mathematical properties.

Findings

Established well-posedness of the PDE system.

Analyzed the asymptotic behavior of solutions.

Handled phase configurations described by singular functions.

Abstract

In this paper we derive, starting from the basic principles of Thermodynamics, an extended version of the nonconserved Penrose-Fife phase transition model, in which dynamic boundary conditions are considered in order to take into account interactions with walls. Moreover, we study the well-posedness and the asymptotic behavior of the Cauchy problem for the PDE system associated to the model, allowing the phase configuration of the material to be described by a singular function.